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The effect of Monte Carlo approximation on coverage error of double‐bootstrap confidence intervals
Author(s) -
Lee S. M. S.,
Young G. A.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00181
Subject(s) - monte carlo method , confidence interval , statistics , bootstrap model , monte carlo integration , mathematics , robust confidence intervals , sampling (signal processing) , interval (graph theory) , quasi monte carlo method , hybrid monte carlo , algorithm , computer science , markov chain monte carlo , combinatorics , physics , filter (signal processing) , boson , particle physics , particle decay , computer vision
A double‐bootstrap confidence interval must usually be approximated by a Monte Carlo simulation, consisting of two nested levels of bootstrap sampling. We provide an analysis of the coverage accuracy of the interval which takes account of both the inherent bootstrap and Monte Carlo errors. The analysis shows that, by a suitable choice of the number of resamples drawn at the inner level of bootstrap sampling, we can reduce the order of coverage error. We consider also the effects of performing a finite Monte Carlo simulation on the mean length and variability of length of two‐sided intervals. An adaptive procedure is presented for the choice of the number of inner level resamples. The effectiveness of the procedure is illustrated through a small simulation study.